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试题原文 |
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(1)a4+64b4 =a4+64b4+16a2b2-16a2b2 =(a2+8b2)2-(4ab)2 =(a2+8b2-4ab)(a2+8b2+4ab); (2)x4+x2y2+y4; =x4+2x2y2+y4-x2y2 =(x2+y2)2-(xy)2 =(x2+y2-xy)(x2+y2+xy); (3)x2+(1+x)2+(x+x2)2 =1+2(x+x2)+(x+x2)2 =(1+x+x2)2; (4)设b-c=x,a-b=y,则c-a=-(x+y), 则(c-a)2-4(b-c)(a-b) =[-(x+y)]2-4xy, =(x-y)2, 所以(c-a)2-4(b-c)(a-b) =(b-c-a+b)2 =(2b-a-c)2; (5)x3-9x+8; =x3-x-8x+8 =(x3-x)-(8x-8) =x(x2-1)-8(x-1) =x(x+1)(x-1)-8(x-1) =(x-1)(x2+x-8); (6)x3+2x2-5x-6 =x3+x2+x2+x-6x-6, =(x3+x2)+(x2+x)-(6x+6) =x2(x+1)+x(x+1)-6(x+1) =(x+1)(x2-x-6) =(x+1)(x+3)(x-2). |
经过对同学们试题原文答题和答案批改分析后,可以看出该题目“把下列各式分解因式:(1)a4+64b4;(2)x4+x2y2+y4;(3)x2+(1+x)2+(..”的主要目的是检查您对于考点“初中因式分解”相关知识的理解。有关该知识点的概要说明可查看:“初中因式分解”。